I don't know how SQL Developer achieves this. Toad does not interact with Kerberos in any way. This all happens at the Oracle client level.
EXTERNAL[PROXYUSERID] is for OS authentication + Oracle Proxy connection. Maybe it will work for you in this case, I'm not sure
When you connect in Toad using EXTERNAL, we send blanks for both username and password to the database, and Oracle's external authentication kicks in.
from This post, 2nd to the last reply:
I don’t have Kerberos here, but to test it I use OS Authentication, which seems to work the same way as far as the database goes. I’ll describe my set up and hopefully it will help you understand what’s going on.
So my windows user in the database ends up being “OPS$PROD\JDORLON” (and I can log in as blank or EXTERNAL with this, without knowing the password). This is your user A.
Now, if I go into the Schema Browser, change object type to USERS, and click on user B in the list, then on the right, on the Proxies tab, I’ll see OPS$PROD\JDORLON. That was set up with this command:
ALTER USER B grant connect through “OPS$PROD\JDORLON”;
With Toad 12.9 and newer, logging in with EXTERNAL[B] (with blank password) works. I don’t get any prompt at all - it just connects. I don’t need to know B’s password because of the proxy grant.